When cathode ray tubes are used to display images, certain well-known geometrical distortions arise which must be compensated for in order for the images to be acceptable. Pincushion distortion causes the straight edges of the nominally rectangular image area to become concave with the four corners displaced outwards. S-distortion causes objects in the peripheral portion of the image to be magnified relative to similar objects in the central portion. Pincushion and S-distortion arise from a common cause; when an electron beam in a cathode ray tube is deflected by a changing magnetic field, the distance along the screen which the point of electron impact travels is not proportional to the magnetic field but increases in a superlinear manner with increasing angle of deflection.
Two factors are involved in producing this lack of proportionality. The first is the fact that the more the beam is deflected., the longer it remains within the yoke; therefore, the deflection angle increases in a superlinear manner with field intensity. The second is the relationship between screen radius and throw distance. If the screen were a sphere whose center coincided with the center of deflection, spot travel would be proportional to deflection angle. But practical screens have longer radii, with the result that spot travel is superlinear with respect to deflection angle, compounding the error produced by the first factor. If the screen is flat, spot travel is proportional to the tangent of the deflection angle, neglecting the forward movement of the center of deflection which is generally small.
FIG. 1 illustrates these relationships for the case of a maximum horizontal deflection angle of plus and minus 39 degrees and a flat screen. Maximum horizontal deflection requires a magnetic field in the deflection yoke which may, for example, be 44 gauss. In this condition, the electron spot appears at the right end of the horizontal axis (point E in FIG. 1), spaced one-half the length of that axis or 5.6 inches on a 14 inch screen from the center C of the viewing area.
If the magnetic field is now reduced to 22 gauss, i.e. one-half of its former value, the deflection angle decreases to 18 degrees, i.e. less than one-half of the original 39 degrees. The electron spot moves inward to position D, spaced only 2.30 inches from the center C; one-half the distance to point E would be 2.80 inches. This non-linear behavior with respect to the magnetic deflection field is duplicated on the left side of the screen, as indicated in FIG. 1 by points E' and D'.
FIG. 2 shows the same screen in plan view and includes an additional point P in the upper right corner. To place the electron spot into position P, a 40 gauss field for horizontal deflection and a 30 gauss field for vertical deflection must be present simultaneously. For comparison, the field needed to place the electron spot at E, directly below P, is 44 gauss. This is not the same as the 40 gauss component required for horizontal deflection in the presence of an orthogonal component of 30 gauss needed to place the spot at P. Evidently, horizontal and vertical non-linearity effects are interdependent. Conventional deflection circuits take account of this interdependence; for example, in the horizontal deflection system, not only is the basically linear sawtooth waveform of the yoke current modified to correct for S-distortion, but the amount of that correction as well as the overall amplitude of the sawtooth are modulated with a parabola at the vertical scanning rate so as to compensate for the above-mentioned interdependence. Similar corrections are imposed upon the vertical waveform. The circuits needed to generate these complex waveforms are costly and require critical adjustments; in addition, modulating and predistorting the horizontal scanning waveform involves the handling of considerable power.
These remarks apply fully to deflection yokes that produce uniform magnetic fields. So called self-convergent yokes, designed to produce astigmatic fields, tend to reduce the need for correction of the vertical waveform and in some cases make such correction unnecessary. At the same time, however, the required corrections for the horizontal waveform become even larger. In all cases, the need for corrections with respect to both horizontal and vertical waveforms increases with cathode ray tubes having a flat screen, thereby burdening this highly desirable tube design with more costly deflection circuits.